If you are disqualified from driving and you feel the punishment is too severe, then do not take a chance by driving during the period of the ban.
Instead lodge your appeal and go via the proper channels. Although it is not impossible to do this on your own, if you have not already instructed a solicitor/lawyer, this is probably the time to do so.

If your case was initially dealt with in the Magistrates' Court, your right of appeal is to the Crown Court.
At that hearing a Judge will review the merits of the case and can either uphold the original decision, rescind it there and then or send the case back to the Magistrates' Court to have it re–heard.

It is possible to get the disqualification suspended, pending the hearing of the appeal.
You will need to apply immediately to the Magistrates' Court for the disqualification to be suspended.
You can do this as soon as the case is concluded or any time thereafter prior to the Crown Court hearing.
However, you can only drive if the Magistrates grant your application.
For hearings in Scotland, the application will be dealt with in the District Court / Sheriff's Court / Justice of the Peace Court.

You can appeal against both the decision to convict you of an offence or the punishment imposed.
If, for example, you have pleaded guilty but were hoping for a more lenient outcome, you would only need to appeal against the sentence, not the conviction.
Whereas if you felt you had been wrongly convicted, you could appeal against both aspects.

Although you can lodge an appeal, the most prudent approach would be to ask for the case to be re–heard.
If you explain to the Court that you were unaware of the original hearing date, the case will probably be relisted without you having to lodge and go through a formal appeal process.

If your application is successful and results in the original decision being altered, you should be able to recover the vast majority, if not all of the costs incurred.
However, costs can be assessed by the Court and they will only allow what is felt to be reasonable for the nature of the case and the action taken.

The fact that you did not seek legal advice is not itself grounds for altering the decision.
Likewise, the case is not going to be relisted simply because you did not arrange representation or assistance in advance of the hearing.
The best way forward would be to seek guidance now and if it is apparent that the outcome can be altered, an appeal can then be lodged.
However, it is feasible that if the application is successful, you may not recover all of your costs on the basis that the Court could conclude that these costs would have been avoided had the case been correctly prepared for the first hearing.

You can apply for your driving licence to be reinstated.
However, this cannot be done if the ban is for less than 2 years.
Additionally, for bans in excess of 2 years, you have to have served at least 2 years or 50%, whichever is the longer.
For bans of 10 years or more, you can apply for reinstatement after 5 years.